An analytical method for the investigation of special types of dispersion relations is presented. In particular, analysis of the propagation of small- amplitude hydromagnetic waves in a collisionless plasma in a strong magnetic field leads to such dispersion relations. The fifth-degree dispersion relation corresponding to a particular case is considered. The necessary stability condition for a steady state and conditions for the degeneration of small- amplitude waves are derived. A comparison with other methods for the analysis of similar dispersion relations is also presented.

Magnetization due to a magnetic moment contributes to the non-oscillating magnetic field in a plasma. The dynamics ofclassically bound electrons in the presence of an applied circularly polarized strong electromagnetic field in the reflection region generates this field. The special case of its resonant generation when the frequency of a right circularlypolarized wave is equal to the ion gyration frequency is studied here. Another source of non-oscillating magnetization isthe interaction of electromagnetic fields, including fields in the Alfvén-wave frequency range, with a cold collisionless fully ionized magnetized plasma also in the reflection region. The induced field from a left circularly polarized field at Alfvén-wave frequencies is paramagnetic, inversely proportional to the square of the ambient field and independent of the mass per particle of both electrons and ions. The induced field from a right circularly polarized field at Alfvén-wave frequencies is diamagnetic, inversely proportional to the cube of the ambient field and depends directly on the plasma mass density.

A thermodynamic analysis of tokamak plasmas is developed, starting from a single-fluid model. Some general propertiesof entropy production in the plasma are discussed. An approach is employed that is more general than the one based on Onsager symmetry relationships. This choice appears to be justified by experiments. The concept of ‘thermodynamic stability’ is introduced, and a general criterion for the stability of stationary states far from thermodynamic equilibrium is assessed. An upper limit on the particle density is found to exist as a necessary condition in order to prevent disruptions. Analysis of the entropy balance shows that this limit is modified when neutral-beam heating is applied. Radial temperature profiles are shown to be stable against external heating under specific experimental conditions, inparticular when ion and electron temperatures are comparable. An offset scaling law for the energy confinement time TE = TE(Pinp) (with Pinp total input power) is obtained for stationary states when stability against additional heating is imposed.

The nonlinear evolution of ion-acoustic waves in a multi-component plasma with negative ions has been studied experimentally using a double-plasma device. At a critical concentration of negative ions the phase velocity of the ion- acoustic waves increases with the wave amplitude, and the wave has negative dispersion, which show that the wave satisfies Lighthill's condition. The initial small modulation in amplitude is found to grow spatially. The observed phenomena are compared with the relevant theory using the nonlinear Schrödinger equation. The fluid equations are integrated to confirm the validity of the nonlinear Schrödinger equation.

In d.c. discharges the Bohm condition is the condition for sheath formation, the ion velocity at the plasma boundary having to satisfy the condition ½Mv2 = ½kB Te, if the spread of velocities is ignored. The model is a good one if the Debye distance is small compared with the relevant scale length. As there is much current interest in radio-frequency (RF) discharges, the question arises as to whether the criterion remains valid in the presence of RF fields. The question has been studied recently by Riemann, following earlier work by Allen who compared the plasma boundary to a sonic surface. Riemann considered a wider range of frequencies and obtained a dispersion relation that was a quartic equation. The present paper examines the complex roots of this equation, using a method developed by Briggs. The results substantiate Riemann's statement that the Bohm criterion is still valid in the presence of RF fields.

This paper outlines a theory of absorption of lower-hybrid (LH) waves in an electron plasma that is based on the nonlinear relation between grad │E3│2, where E3 is the electric field component parallel to the external homogeneous magnetic field, and the space dependent quasi-linear diffusion coefficient, and consequently between grad │E3│2 and the absorption. A local absorption induces an increase of the value of the gradient in the neighbouring region and thereby extends the absorption domain. In this way virtually total ‘single-path’ absorption of the injected LH power is obtained. The theory also allows an explanation of the density limit in current drive.

A standard theory of strong scintillations in an isotropic medium is extended to the case of polarized radiation propagating through a weakly anisotropic, randomly inhomogeneous, magnetized plasma. A hierarchy of moments of the radiationfield is defined, with an nth-order moment being an nth-rank polarization tensor, and the tensor equation for the evolution of an arbitrary moment is derived. Emphasis isplaced on the mutual coherence function (a second moment), which is rewritten in terms of the Stokes parameters. The evolution of the polarized radiation through the randomly inhomogeneous, weakly anisotropic medium is described in terms ofa matrix equation for the Stokes vector. It is shown that the theory implies that a depolarization occurs as a result ofsuch propagation. This corresponds to a decrease in the degree of linear polarization for propagation through a weakly anisotropic plasma. The rate of depolarization is estimated, and an interpretation is suggested. The polarization dependence of the angular size of the apparent image is determined. Two counter-intuitive results are found: that the image canhave a circularly polarized component even for an unpolarized source, and that the angular size of the linearly polarized source can decrease. These are interpreted in terms of random variations in the ray path with opposite signs for the two natural modes, resulting in a separation of the centroids of the images in the two circular polarizations.

The theory of strong scintillations in a weakly anisotropic plasma is used to derive an equation satisfied by the correlation functions for the Stokes parameters. The coefficients that describe these correlation functions are determined explicitly in terms of a matrix generalization of the standard phasestructure function. In discussing implications of the theory, emphasis is placed on terms that have no counterpart in an isotropic plasma. It is shown that the decay of the linear polarizaiton that results from differential Faraday rotation is different in the mean squares and the square means of the Stokes parameters. In principle, this allows one to determine properties relating to the fluctuations of the magnetic field along the ray path. A formal treatment of polarization dependent intensity fluctuations in a magnetized plasma is presented and discussed briefly.

The asymptotic theory of flows of high-pressure plasmas past biased bodies (electrostatic probes) is extended to relatively low charge densities, where the Debye radius h is comparable to or exceeds the thickness ▴ of the viscous near- probe boundary layer. Various orders of magnitude of h with respect to a dimension of the probe and various ranges of the probe potential are considered. The governing physical mechanism of current transfer in the perturbation region is identified in each regime, and simple formulae for the probe current–voltage characteristic are obtained whenever possible. In particular, it is shown that an earlier conclusion, valid for h ≪ Δ, on the existence of a linear segment on the electron branch of current-voltage characteristic with a slope depending on the electron density, is also valid in the present situation. It h ≫ Δ, a similar conclusion holds for the ion branch; at large enough probe potentials the jon branch saturates —although for a different physical reason than in the case h ≪ Δ

The spatial factor Φ(x) of the vibratory-state MWB (‘multiple water-bag’) plasma potential Φ = Φ(x) exp (- iwt) in the vicinity of its generating electric charge rgr;(x) exp (- iwt) is proved to be the Poisson potential U(x) of ρ plus an error function ξ(x) whose magnitude can be rendered as small as desired, in relation to │Φ(x)│, by locating the recording point sufficiently close to the charge. How close this should be is independent of ρ, but depends quantitatively on the MWB model and the frequency ω, and qualitatively on whether the frequency of the vibrations is greater or less than the plasma frequency. A high vibration frequency reinforces accuracy in the Poissonian approximation. The question as to whether Φ is weaker or stronger than U(x) is tacked. Shielding efficiency is explored in the vibratory state.

The generation of a quasi-stationary nonlinear magnetization current in a plasma in the presence of high-frequency electromagnetic waves is considered. A kinetic theory is developed that takes the velocity dependence of the collision frequency into account. The results show that even a small collision term can have a significant effect on the generation mechanism.

A helical ion beam propagating through a plasma cylinder drives electrostatic ion-cyclotron waves to instability via cyclotron interaction. Higher harmonics of the beam cyclotron frequency can be generated in this way. The growth rate increases with the harmonic number. The efficiency of beam energy transfer to the wave can be of the order of a few per cent.

A high-power millimetre wave (w1, k1) propagating through a magnetized plasma in the presence of a wiggler magnetic field (0, k0) produces density perturbations at (w1, K1 +K0). The density perturbations couple with the oscillatory velocity at (wl, K1) to produce a nonlinear current at (2w1, 2K1 +K0) driving second-harmonic electromagnetic radiation. The amplitude of the generated wave is sensitive to cyclotron resonance.